Mani & Walkup's 3sphere(D)
 Description

Mani and Walkup's 3sphere which is not vertex decomposable.
This example is made from their another sphere (maniwalkupC.dat) to reduce the number of faces a little.
Called "D" in the paper.
 Properties

In the paper, it is written that whether this 3sphere is shellable
or not known to the authors.
But my recent calculation on the computer showed that this sphere is
shellable. Here is a shelling.
 Datum

maniwalkupD.dat
 Some table

vertex decomposable?  no 
extendably shellable?  ? 
shellable?  open problem yes 
constructible?  ? 
CohenMacaulay?  yes 
partitionable?  yes 
topology  3sphere 
fvector  (1,16,106,180,90) 
hvector  (1,12,64,12,1) 
made by  Mani&Walkup 
 References
 P.Mani and D.W.Walkup,
A 3sphere counterexample to the $W_v$path conjecture,
Math. Operations Research 5 (1980), 595598.
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